Citation for this paper:
Abe, K.; Amey, J.; Andreopoulos, C.; Antonova, M.; Aoki, S.; Ariga, A.; … & Zito, M. (2017). Measurement of ¯
νμ
andνμ
charged current inclusive cross sections and their ratio with the T2K off-axis near detector. Physical Review D, 96(5), article 52001.UVicSPACE: Research & Learning Repository
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Faculty of Science
Faculty Publications
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Measurement of ¯
νμ
andνμ
charged current inclusive cross sections and their ratio with the T2K off-axis near detectorK. Abe et al. (The T2K Collaboration) September 2017
© 2017. This is an open access article published under the terms of the Creative Commons Attribution 4.0 International License. http://creativecommons.org/licenses/by/4.0
This article was originally published at:
Measurement of
¯ν
μand
ν
μcharged current inclusive cross sections
and their ratio with the T2K off-axis near detector
K. Abe,45 J. Amey,15 C. Andreopoulos,43,25 M. Antonova,20 S. Aoki,22A. Ariga,1 Y. Ashida,23 S. Ban,23 M. Barbi,37 G. J. Barker,53 G. Barr,33 C. Barry,25 M. Batkiewicz,11 V. Berardi,16 S. Berkman,3,49 S. Bhadra,57 S. Bienstock,34
A. Blondel,10 S. Bolognesi,5 S. Bordoni,13,* S. B. Boyd,53 D. Brailsford,24 A. Bravar,10 C. Bronner,45 M. Buizza Avanzini,9 R. G. Calland,21 T. Campbell,7 S. Cao,12 S. L. Cartwright,41 M. G. Catanesi,16 A. Cervera,14
A. Chappell,53 C. Checchia,18 D. Cherdack,7 N. Chikuma,44 G. Christodoulou,25 J. Coleman,25 G. Collazuol,18 D. Coplowe,33A. Cudd,27A. Dabrowska,11G. De Rosa,17T. Dealtry,24P. F. Denner,53S. R. Dennis,25C. Densham,43
F. Di Lodovico,36 S. Dolan,33 O. Drapier,9 K. E. Duffy,33 J. Dumarchez,34 P. Dunne,15 S. Emery-Schrenk,5 A. Ereditato,1 T. Feusels,3,49 A. J. Finch,24 G. A. Fiorentini,57 M. Friend,12,† Y. Fujii,12,† D. Fukuda,31 Y. Fukuda,28
A. Garcia,13 C. Giganti,34 F. Gizzarelli,5 T. Golan,55 M. Gonin,9 D. R. Hadley,53 L. Haegel,10 J. T. Haigh,53 D. Hansen,35 J. Harada,32 M. Hartz,21,49 T. Hasegawa,12,† N. C. Hastings,37 T. Hayashino,23 Y. Hayato,45,21 A. Hillairet,50 T. Hiraki,23 A. Hiramoto,23 S. Hirota,23 M. Hogan,7 J. Holeczek,42 F. Hosomi,44 K. Huang,23 A. K. Ichikawa,23M. Ikeda,45J. Imber,9 J. Insler,26 R. A. Intonti,16T. Ishida,12,† T. Ishii,12,† E. Iwai,12K. Iwamoto,44
A. Izmaylov,14,20 B. Jamieson,54 M. Jiang,23 S. Johnson,6 P. Jonsson,15 C. K. Jung,30,‡ M. Kabirnezhad,29 A. C. Kaboth,39,43 T. Kajita,46,‡ H. Kakuno,47 J. Kameda,45 D. Karlen,50,49 T. Katori,36 E. Kearns,2,21,‡ M. Khabibullin,20 A. Khotjantsev,20 H. Kim,32 J. Kim,3,49 S. King,36 J. Kisiel,42 A. Knight,53 A. Knox,24 T. Kobayashi,12,† L. Koch,40 T. Koga,44 P. P. Koller,1 A. Konaka,49 L. L. Kormos,24 Y. Koshio,31,‡ K. Kowalik,29 Y. Kudenko,20,§ R. Kurjata,52 T. Kutter,26 J. Lagoda,29 I. Lamont,24 M. Lamoureux,5 P. Lasorak,36 M. Laveder,18
M. Lawe,24 M. Licciardi,9 T. Lindner,49 Z. J. Liptak,6 R. P. Litchfield,15 X. Li,30 A. Longhin,18 J. P. Lopez,6 T. Lou,44 L. Ludovici,19 X. Lu,33 L. Magaletti,16 K. Mahn,27 M. Malek,41 S. Manly,38 L. Maret,10 A. D. Marino,6
J. F. Martin,48 P. Martins,36 S. Martynenko,30 T. Maruyama,12,† V. Matveev,20 K. Mavrokoridis,25 W. Y. Ma,15 E. Mazzucato,5 M. McCarthy,57 N. McCauley,25 K. S. McFarland,38 C. McGrew,30 A. Mefodiev,20 C. Metelko,25 M. Mezzetto,18 A. Minamino,56 O. Mineev,20 S. Mine,4 A. Missert,6 M. Miura,45,‡ S. Moriyama,45,‡ J. Morrison,27
Th. A. Mueller,9 T. Nakadaira,12,† M. Nakahata,45,21 K. G. Nakamura,23 K. Nakamura,21,12,† K. D. Nakamura,23 Y. Nakanishi,23 S. Nakayama,45,‡ T. Nakaya,23,21 K. Nakayoshi,12,† C. Nantais,48 C. Nielsen,3,49 K. Nishikawa,12,†
Y. Nishimura,46 P. Novella,14 J. Nowak,24 H. M. O’Keeffe,24 K. Okumura,46,21 T. Okusawa,32 W. Oryszczak,51 S. M. Oser,3,49 T. Ovsyannikova,20 R. A. Owen,36 Y. Oyama,12,† V. Palladino,17 J. L. Palomino,30 V. Paolone,35
N. D. Patel,23 P. Paudyal,25 M. Pavin,34 D. Payne,25 Y. Petrov,3,49 L. Pickering,15 E. S. Pinzon Guerra,57 C. Pistillo,1 B. Popov,34,∥ M. Posiadala-Zezula,51 J.-M. Poutissou,49 A. Pritchard,25 P. Przewlocki,29 B. Quilain,23 T. Radermacher,40 E. Radicioni,16 P. N. Ratoff,24 M. A. Rayner,10 E. Reinherz-Aronis,7 C. Riccio,17 E. Rondio,29
B. Rossi,17 S. Roth,40 A. C. Ruggeri,17 A. Rychter,52 K. Sakashita,12,† F. Sánchez,13 E. Scantamburlo,10 K. Scholberg,8,‡ J. Schwehr,7 M. Scott,49 Y. Seiya,32 T. Sekiguchi,12,† H. Sekiya,45,21,‡ D. Sgalaberna,10 R. Shah,43,33
A. Shaikhiev,20 F. Shaker,54 D. Shaw,24 M. Shiozawa,45,21 T. Shirahige,31 M. Smy,4 J. T. Sobczyk,55 H. Sobel,4,21 J. Steinmann,40 T. Stewart,43 P. Stowell,41 Y. Suda,44 S. Suvorov,20 A. Suzuki,22 S. Y. Suzuki,12,† Y. Suzuki,21
R. Tacik,37,49 M. Tada,12,† A. Takeda,45 Y. Takeuchi,22,21 R. Tamura,44 H. K. Tanaka,45,‡ H. A. Tanaka,48,49,¶ T. Thakore,26 L. F. Thompson,41 S. Tobayama,3,49 W. Toki,7 T. Tomura,45 T. Tsukamoto,12,† M. Tzanov,26
M. Vagins,21,4 Z. Vallari,30 G. Vasseur,5 C. Vilela,30 T. Vladisavljevic,33,21 T. Wachala,11 C. W. Walter,8,‡ D. Wark,43,33 M. O. Wascko,15 A. Weber,43,33 R. Wendell,23,‡ M. J. Wilking,30 C. Wilkinson,1 J. R. Wilson,36 R. J. Wilson,7 C. Wret,15 Y. Yamada,12,† K. Yamamoto,32 C. Yanagisawa,30,** T. Yano,22 S. Yen,49 N. Yershov,20
M. Yokoyama,44,‡ M. Yu,57 A. Zalewska,11 J. Zalipska,29 L. Zambelli,12,† K. Zaremba,52 M. Ziembicki,52 E. D. Zimmerman,6 and M. Zito5
(The T2K Collaboration)
1University of Bern, Albert Einstein Center for Fundamental Physics, Laboratory for High Energy Physics
(LHEP), Bern, Switzerland
2Boston University, Department of Physics, Boston, Massachusetts, USA 3
University of British Columbia, Department of Physics and Astronomy, Vancouver, British Columbia, Canada
4
University of California, Irvine, Department of Physics and Astronomy, Irvine, California, USA
5IRFU, CEA Saclay, Gif-sur-Yvette, France 6
University of Colorado at Boulder, Department of Physics, Boulder, Colorado, USA
7Colorado State University, Department of Physics, Fort Collins, Colorado, USA
8Duke University, Department of Physics, Durham, North Carolina, USA 9
Ecole Polytechnique, IN2P3-CNRS, Laboratoire Leprince-Ringuet, Palaiseau, France
10University of Geneva, Section de Physique, DPNC, Geneva, Switzerland 11
H. Niewodniczanski Institute of Nuclear Physics PAN, Cracow, Poland
12High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki, Japan 13
Institut de Fisica d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, Bellaterra (Barcelona) Spain
14
IFIC (CSIC & University of Valencia), Valencia, Spain
15Imperial College London, Department of Physics, London, United Kingdom
16
INFN Sezione di Bari and Università e Politecnico di Bari, Dipartimento Interuniversitario di Fisica, Bari, Italy
17
INFN Sezione di Napoli and Università di Napoli, Dipartimento di Fisica, Napoli, Italy
18INFN Sezione di Padova and Università di Padova, Dipartimento di Fisica, Padova, Italy 19
INFN Sezione di Roma and Università di Roma“La Sapienza,” Roma, Italy
20Institute for Nuclear Research of the Russian Academy of Sciences, Moscow, Russia 21
Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study, University of Tokyo,
Kashiwa, Chiba, Japan
22Kobe University, Kobe, Japan 23
Kyoto University, Department of Physics, Kyoto, Japan
24Lancaster University, Physics Department, Lancaster, United Kingdom 25
University of Liverpool, Department of Physics, Liverpool, United Kingdom
26Louisiana State University, Department of Physics and Astronomy,
Baton Rouge, Louisiana, USA
27Michigan State University, Department of Physics and Astronomy, East Lansing, Michigan, USA 28
Miyagi University of Education, Department of Physics, Sendai, Japan
29National Centre for Nuclear Research, Warsaw, Poland 30
State University of New York at Stony Brook, Department of Physics and Astronomy, Stony Brook, New York, USA
31
Okayama University, Department of Physics, Okayama, Japan
32Osaka City University, Department of Physics, Osaka, Japan 33
Oxford University, Department of Physics, Oxford, United Kingdom
34UPMC, Université Paris Diderot, CNRS/IN2P3, Laboratoire de Physique Nucléaire et de Hautes
Energies (LPNHE), Paris, France
35University of Pittsburgh, Department of Physics and Astronomy,
Pittsburgh, Pennsylvania, USA
36Queen Mary University of London, School of Physics and Astronomy, London, United Kingdom
37
University of Regina, Department of Physics, Regina, Saskatchewan, Canada
38University of Rochester, Department of Physics and Astronomy, Rochester, New York, USA 39
Royal Holloway University of London, Department of Physics, Egham, Surrey, United Kingdom
40RWTH Aachen University, III. Physikalisches Institut, Aachen, Germany 41
University of Sheffield, Department of Physics and Astronomy, Sheffield, United Kingdom
42University of Silesia, Institute of Physics, Katowice, Poland 43
STFC, Rutherford Appleton Laboratory, Harwell Oxford, and Daresbury Laboratory, Warrington, United Kingdom
44
University of Tokyo, Department of Physics, Tokyo, Japan
45University of Tokyo, Institute for Cosmic Ray Research,
Kamioka Observatory, Kamioka, Japan
46University of Tokyo, Institute for Cosmic Ray Research, Research Center for Cosmic Neutrinos,
Kashiwa, Japan
47Tokyo Metropolitan University, Department of Physics, Tokyo, Japan 48
University of Toronto, Department of Physics, Toronto, Ontario, Canada
49TRIUMF, Vancouver, British Columbia, Canada
50
University of Victoria, Department of Physics and Astronomy, Victoria, British Columbia, Canada
51
University of Warsaw, Faculty of Physics, Warsaw, Poland
52Warsaw University of Technology, Institute of Radioelectronics, Warsaw, Poland 53
University of Warwick, Department of Physics, Coventry, United Kingdom
54University of Winnipeg, Department of Physics, Winnipeg, Manitoba, Canada 55
56Yokohama National University, Faculty of Engineering, Yokohama, Japan 57
York University, Department of Physics and Astronomy, Toronto, Ontario, Canada (Received 15 June 2017; published 5 September 2017)
We report a measurement of cross sectionσðνμþ nucleus → μ−þ XÞ and the first measurements of the cross sectionσð¯νμþ nucleus → μþþ XÞ and their ratio Rðσð¯νÞσðνÞÞ at (anti) neutrino energies below 1.5 GeV. We determine the single momentum bin cross section measurements, averaged over the T2K¯ν=ν-flux, for the detector target material (mainly carbon, oxygen, hydrogen and copper) with phase space restricted
laboratory frame kinematics of θμ< 32° and pμ> 500 MeV=c. The results are σð¯νÞ ¼
ð0.900 0.029ðstatÞ 0.088ðsystÞÞ × 10−39 and σðνÞ ¼ ð2.41 0.022ðstatÞ 0.231ðsystÞÞ × 10−39 in
units of cm2=nucleon and Rðσð¯νÞσðνÞÞ ¼ 0.373 0.012ðstatÞ 0.015ðsystÞ. DOI:10.1103/PhysRevD.96.052001
I. INTRODUCTION
Since the 1998 discovery [1]of neutrino oscillations, there have been major advances in neutrino disappearance and appearance oscillation measurements, and all the fundamental neutrino mixing parameters [2] have been determined except for the mass hierarchy and the charge-parity (CP) phase δCP. Evidence ofδCP≠ 0; π leads to the nonconservation or violation of the charge-parity sym-metry (CPV). This is tested by measuring the neutrino νμ→ νe and antineutrino ¯νμ→ ¯νe appearance oscillation
event rates to determine if the neutrino and antineutrino oscillation appearance probabilities, Pðνμ→ νeÞ and ¯Pð¯νμ→ ¯νeÞ are equal in vacuum [2,3]at the same ratio
of the oscillation distanceL over the neutrino energy E or
L
E. Major long-baseline neutrino experiments [4] have
been built and future projects [5] are proposed to determine these probabilities using separate νμ and ¯νμ beams that cross near and far detectors. The probabilities are obtained from near detector measurements of the νμþ N and ¯νμþ N charged current (CC) interactions and
cross sections, where N is the target nucleon, and far detector measurements of νeþ N and ¯νeþ N CC interactions.
In this paper, the T2K Collaboration, using the off-axis near detector (ND280), presents a measurement at a peak energy∼0.6 GeV of the charged current inclusive (CCINC) νμþ N cross section and first CCINC measurements of the
¯νμþ N cross section and their ratio of the ¯νμþ N over the
νμþ N CCINC cross section. These νμand¯νμmeasurements
are important to understand their impact on future CPV measurements and to test neutrino cross section models.
T2K has published flux averaged neutrino-mode mea-surements of CCINC[6]and charged current quasi-elastic like (CCQE) [7] cross sections per nucleon of ð6.91 0.13ðstatÞ 0.84ðsystÞÞ × 10−39 cm2 and ð4.15 0.6Þ×
10−39 cm2, respectively. These measurements were
per-formed using the Fine-Grain Detector (FGD) which has different detector systematics compared to the measure-ments presented in this paper. There are no published CCINC ¯νμ measurements at energies below 1.5 GeV; however, the MINVERVA Collaboration recently pub-lished [8] CCINC results above 2 GeV and the MiniBooNE Collaboration has published[9]CCQE mea-surements in both ¯νμ and νμ modes which require larger axial mass values compared to other experiments to fit their observed data. There are several multinucleon models (2 particle 2 hole, or 2p2h)[10–12]proposed to explain large cross sections. In addition, in some models it has been predicted [10] that the difference between the νμ and ¯νμ cross sections is expected to increase when 2p2h effects
[13]are included. The measurements of the ratio, sum, and difference of these cross sections, which have very different systematic errors, will be presented.
Following this introduction, the paper is organized as follows. We begin with a description of the ND280 off-axis detector and the neutrino beam in Sec. II. Then the Monte Carlo (MC) simulation is presented in Sec. III, followed by the event selection given in Sec. IV. The analysis methods and systematic error evaluations are presented in Secs.VandVI, and we finally conclude with the results and conclusions in Secs.VII andVIII.
*Now at CERN.
†Also at J-PARC, Tokai, Japan.
‡Affiliated member at Kavli IPMU (WPI), the University of
Tokyo, Japan.
§Also at National Research Nuclear University "MEPhI" and
Moscow Institute of Physics and Technology, Moscow, Russia.
∥Also at JINR, Dubna, Russia.
¶Also at Institute of Particle Physics, Canada.
**Also at BMCC/CUNY, Science Department, New York,
New York, USA.
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
II. BEAM AND DETECTOR
The T2K experiment [14] is composed of a neutrino beam line and a near detector at the J-PARC laboratory in Tokai, Japan, and the far detector Super-Kamiokande (SK) situated 295 km away in the Kamioka mine. The J-PARC accelerator complex produces a 30 GeV energy proton beam with spills every 2.48 s that contain eight beam bunches which are 580 ns apart. At this spill and repetition rate, a beam power of 430 kW produces 2.25 × 1014 protons on target (PoT) per spill corresponding to ≈0.8 × 1019 PoT integrated per day of data taking.
The proton beam strikes a graphite target to produce pions and kaons that are focused by three magnetic horns into a 96 m long decay pipe. The polarity of the magnetic horns can be changed to forward horn current (FHC) or reverse horn current (RHC) to select either positive or negative pions and kaons to produce a predominantly νμ or an ¯νμ beam. The resulting main neutrino beam axis is parallel to the proton beam direction. SK lies 2.5° off-axis with respect to the main neutrino beam direction and this arrangement produces at SK both the νμ and ¯νμ energies that peak at ∼0.6 GeV. This νμð¯νμÞ peak energy with a 295 km baseline distance, produces an LEvalue that max-imizes the νeð¯νeÞ appearance rate and has a νμð¯νμÞ disappearance that minimizes theνμð¯νμÞ rates at SK.
The ND280 νμ and ¯νμ fluxes were determined by simulation of the T2K neutrino beam line [15] using FLUKA2011 [16], GEANT [17], and GCALOR [18]
software packages. The simulated hadronic yields have been re-weighted using the NA61/SHINE [19]thin-target data, which has reduced the flux uncertainties to less than 10% around the flux peak. Detailed descriptions of the ND280 flux uncertainties have been published in previous ND280 analyses [20]. The typical fractional covariance error of the T2Kνμand¯νμfluxes are∼10% and the νμ− ¯νμ correlated flux errors are∼6%. The νμand¯νμflux rates per cm2=50 MeV=1021 PoT are plotted in Fig.1 with super-imposed neutral lepton flavors, νμ,νe, ¯νμ and ¯νe.
The near detector complex, located 280m downstream of the target, consists of an on-axis detector (INGRID) and the ND280 off-axis detector. ND280 is positioned inline between the neutrino beam target and SK. The ND280 detector consists of subdetectors inside the refurbished UA1/NOMAD magnet that operates at a 0.2 T magnetic field whose direction is horizontal and perpendicular to the neutrino beam. The ND280 subdetectors includeπ0 detec-tor [21] (P∅D), three tracking time projection chambers
[22] (TPC1,2,3), two fine-grained detectors (FGD1,2) interleaved with TPC1,2,3, and an electromagnetic calo-rimeter (ECAL), that encloses the P∅D, TPC1-3 and FGD1-2 subdetectors.
The measurements in this paper used the P∅D and the TPC tracking subdetectors in the ND280 detector complex. In our description, theþ Z direction is parallel to the
neutrino beam direction, and theþ Y direction is vertically upwards. Previous descriptions of analyses using the P∅D have been published[23]. We describe additional details relevant for the analysis presented in this paper.
The P∅D is shown in Fig.2. This detector contains 40 scintillator module planes called P∅Dules. Each P∅Dule has 134 horizontal and 126 vertical triangular scintillator bars. A wavelength shifting fiber centered in each bar is readout on one end by a silicon photomultiplier. The P∅D dimensions are2298 × 2468 × 2350 mm3—XYZ—with a total mass of ∼1900 kg of water and 3570 kg of other materials (mainly scintillator with thin layers of high density polyethylene plastic and brass sheet). The target
FIG. 1. The predominately neutrino FHC beam (Top) and
predominately antineutrino RHC beam (Bottom) flux per PoT as a function of energy at the ND280 detector. The rates are separated by neutrino/antineutrino muon and electron type flavors. The peak values for the neutrino and the antineutrino flux rates are 1.7 × 1012 and 1.4 × 1012=cm2=50 MeV=1021 PoT, respectively.
material mass is given in fractional amounts in Table I. These P∅Dules are formed into three major sections. The water target region, is the primary target in this analysis which has 26 P∅Dules interleaved with bags of water 2.8 cm thick and 1.3 mm brass sheets. The water bags are drainable to allow water target subtraction measurements. The two other regions (called upstream and central ECALs) are the upstream and downstream sections that each contain 7 P∅Dules and steel sheets clad with lead (4.9 radiation lengths).
The TPC1,2,3 detectors are three modules whose dimensions are each 1808 × 2230 × 852 mm3—XYZ— where each module contains a centered high voltage (Z-Y) cathode plane that splits the chamber into two sections where the charged particle track ionizations drift in theX directions. These are measured by 70 mm2 micro-megas pads in the Z-Y plane. The fully contained ionized track path lengths are 72 cm. A charged track will be measured with ∼0.7 mm resolution for drift distances >10 cm. The typical TPC momentum resolution is δðp⊥Þ=p⊥ ¼ 0.08p⊥ ðGeV=cÞ. Analyses which use the TPC have been
described in previous ND280 publications[20]. III. ANALYSIS SAMPLES
The studies reported here includes data logged with the FHCν beam runs (October 2012 to February 2013) and the RHC ¯ν beam runs (May 2014 to June 2014).
A. Data samples and detector configuration The total PoT exposure where all detector data quality checks were passed for the FHC runs was16.24 × 1019and the corresponding total PoT exposure for the RHC runs was 4.30 × 1019. These integrated rates corresponds to roughly
0.28 × 1012 neutrinos and 0.06 × 1012 antineutrinos per
cm2per 50 MeV at 0.6 GeV. The data samples in this paper used the available neutrino and antineutrino beam data taken when the P∅D target bags were filled with water.
B. Monte Carlo simulation
The analysis used simulated MC samples with different beam and detector configurations for each data-taking period. The simulations include the following:
(1) Secondary pions and kaons are produced in the graphite target and propagated through the magnetic horns into a helium filled pipe where they decay. Secondary neutrinos and antineutrinos are created and their fluxes and energy spectra are extrapolated to the near and far detectors.
(2) The neutrino and antineutrino interactions in the ND280 subdetectors were determined by the NEUT
[24] MC generator that was used to calculate the interaction cross sections and the final state particle kinematics.
(3) The detector simulation uses GEANT to propagate the final state particles through the ND280 subde-tectors.
IV. EVENT AND KINEMATIC SELECTION A. Event selection
The analysis selection uses reconstructed objects from both the P∅D and TPC. Both subdetectors use independent reconstruction algorithms to generate objects from the raw data. The P∅D uses a three-dimensional tracking algorithm
FIG. 2. Side view schematic diagram of the P∅D detector. The white, zig-zag, and blue strip regions represent the vertical scintillator bars, the horizontal scintillator bars, and the water bag regions, respectively. The vertical and horizontal bars represent a X-Y module or P∅Dule. The first and last groups
of seven P∅Dules form the upstream and the central ECAL
“super” modules and the middle 26 P∅Dules interleaved with the water bags are the water target region.
TABLE I. Chemical element composition of P∅D water target
region by fraction of mass.
Element Symbol Fraction
Hydrogen H 8.0% Carbon C 45.0% Oxygen O 29.9% Copper Cu 14.3% Chlorine Cl 1.1% Titanium Ti 0.1% Zinc Zn 1.6%
to form tracks from individual hits in the scintillator bars. The TPC reconstruction uses a track in the Y-Z plane (nondrift plane) as a seed to search for hits in the down-stream FGD to form a track object.
After independent reconstructions in the TPC and in the P∅D, the analysis uses an algorithm to match a three-dimensional P∅D track ending near the most downstream edge of the P∅D to a TPC track beginning near the most upstream edge of the TPC.
The event selection is the following:
(1) The first requirement is good data quality for the data run. After ND280 data is processed, the sub-detectors are evaluated run by run for good timing with respect to the beam and checked to satisfy good detector calibrations. Events are used only if their run passed data quality checks. For each FHC (RHC) beam bunch there must be a negative (positive) TPC track that is identified within 70 ns around the nominal beam bunch time. (2) A veto is applied to reject events whose vertex
originated outside the fiducial region but had a secondary interaction inside the fiducial region. Also events with single tracks that are broken into two tracks by the track reconstruction are rejected. The event vertex is defined by the most upstream P∅Dule hit in the track. The vertex X-Y position is defined by the X-Y triangular scintillator bars and the vertex Z position of the P∅Dule. The fiducial volume requires the vertex to be within −836 mm < X < 864 mm and−871 mm < Y < 869 mm and inside one of the middle 24 P∅Dules. The X boundaries are ∼250 mm and the Y boundaries are∼236 mm away from the ends of the X and Y scintillator bars, respectively. (3) The vertex must be in the P∅D water target fiducial
volume. The charge is determined by the curvature of the TPC track. Of all TPC tracks meeting these criteria, the one with the highest reconstructed
momentum at the start of the track is chosen to be the lepton candidate.
(4) The RHC mode selection has an additional require-ment that the lepton track candidate is positively charged and has the highest momentum of all charged tracks in the bunch.
Due to the limited geometric acceptance of requiring a CC neutrino event vertex in the P∅D with its muon track detected in the TPC, this analysis is inherently not sensitive to the entire muon kinematic phase space. For this reason, we define a restricted phase space, described in the next subsection, that will cover the part of the kinematic phase space where we have good acceptance. Events that are reconstructed to have muon kinematics outside of the restricted phase space will be rejected. For the FHC mode selection, 19,259 events are selected in data. The number of selected events in the corresponding MC sample, scaled to the same data PoT exposure is 19,566. In RHC mode, 1,869 events are selected in data and the scaled MC sample has 1,953 events. The muon p and θ distributions for data events with MC predictions are shown for both modes in Figs.3 (left and middle) and4 (left and middle), respec-tively. The plots include colored stacked histograms of MC interaction types to graphically display the composition of the selected events.
The fractional NEUT interaction types for the FHC and the RHC beam modes are given in TableIIfor the selected events described in Sec.IV. The MC channels defined[25]
at the initial interaction vertex according to NEUT are CCQE (QE), 2p2h, CC with 1 charged pion (1Pi), CC with > 1 charged pion (NPi), CC with K or η meson (Meson), deep inelastic scattering (DIS), neutral current (NC), neutrino or antineutrino interaction (ν or ¯ν), and events whose true vertex position was outside the fiducial volume (outFV) region of the P∅D. The resulting selected events, according to the MC simulation, are predominately CCQE, followed by CC events with 1 pion. Due to a substantialνμ
Momentum (MeV/c) Theta (degree) 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 Events 200 400 600 800 1000 1200 1400 1600 1800 2000 Data QE 2p2h 1Pi NPi Meson DIS NC ν outFV 0 10 20 30 40 50 60 70 80 90 Events 200 400 600 800 1000 1200 1400 1600 1800 Data QE 2p2h 1Pi NPi Meson DIS NC ν outFV Dule ∅ P 0 5 10 15 20 25 30 35 40 Events 200 400 600 800 1000 1200 1400 1600 Data QE 2p2h 1Pi NPi Meson DIS NC ν outFV
FIG. 3. FHC beam CCINCνμ event candidate distributions of theμ− momentum in MeV=c (left), the muon θμ angle in degrees (middle), and interaction vertex position by P∅Dule (right). Note backgrounds in the CCINC sample are the NC (dark green), ¯νμinduced events (yellow) and the out of fiducial volume events (light blue). There are negligible¯νμbackgrounds (yellow) in the FHC sample.
flux contamination in the RHC beam and a largeνμ cross section, the ¯νμ candidate sample has a larger background fraction (see yellow band in Fig. 4) compared to the ¯νμ background events in the FHC beam sample. Theνμin the RHC beam flux is seen in Fig. 1 (Bottom). The outFV backgrounds are roughly the same fraction in both FHC and RHC beam samples. The selection produces a CCINC νμcandidate event sample that is 94.8% pure and a CCINC
¯νμ candidate event sample that is 83.0% pure. The outFV
backgrounds cluster in the light blue bands in Figs.3(right) and 4 (right) in the downstream P∅Dules. These
back-grounds are events whose vertices are outside and down-stream of the fiducial volume but with an interaction that has a backwards going track that enters the fiducial volume. Additional checks between the data and MC event selections were performed by comparing the event rates of vertices by detector P∅Dule between data and
normalized selected MC events. The event rates by P∅Dule are shown for νμ and ¯νμ in Figs. 3(right) and 4
(right), respectively. There is very good agreement within statistics between the data and MC distributions, except the momentum distribution in the FHC beam sample where the data are 1–2 sigma below the MC predictions near 0.6 GeV=c. The efficiency for the νμand ¯νμ events varies
as a function of P∅Dule. Since the event selection requires a vertex in a P∅Dule with a muon track reconstructed in the TPC, the downstream P∅Dules have a higher efficiency than the upstream P∅Dules. The events with vertices in the more upstream P∅Dule have smaller angular acceptance for a muon track to pass through the TPC and the muon track will incur more energy loss since it must pass through more P∅Dules to reach the TPC where it must be reconstructed. The ν event selection efficiency in Fig. 3 (right) from upstream to downstream P∅Dule varies from 37% to 57% whereas the ¯νμ event selection efficiency Fig. 4 (right) varies from 39% to 68%.
B. Kinematic selection
The selected events for the RHC (FHC) samples require a vertex in the P∅D and a μþðμ−Þ reconstructed track in the TPC detector. This limits or restricts the available kinematic phase space of the CCINC events such that certain kinematic regions are not measured. These unmeasured regions in the laboratory frame have low muon momentum pμ< 500 MeV=c or large muon polar angles θμ> 32°.
These kinematic boundaries are displayed in Figs.5and
6left (right) where theθμversuspμtwo-dimensional plots are shown for the RHC (FHC) samples. In Fig.5left (right) are the generated MC full acceptance CCINC events for the RHC (FHC) samples. Theνμ mode has more events with largerθμ polar angles since the μ− angular distribution is more isotropic than the μþ in the ¯νμ mode whose muon Momentum (MeV/c) Theta (degree)
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 Events 50 100 150 200 250 DataQE 2p2h 1Pi NPi Meson DIS NC ν outFV 0 10 20 30 40 50 60 70 80 90 Events 20 40 60 80 100 120 140 160 180 200 DataQE 2p2h 1Pi NPi Meson DIS NC ν outFV Dule ∅ P 0 5 10 15 20 25 30 35 40 Events 20 40 60 80 100 120 140 160 180 DataQE 2p2h 1Pi NPi Meson DIS NC ν outFV
FIG. 4. RHC beam CCINC ¯νμ event candidate distributions of theμþ momentum in MeV/c (left), the muonθμ angle in degrees (middle), and interaction vertex position by P∅Dule (right). Note backgrounds in the CCINC sample are the NC (dark green), νμinduced events (yellow) and the out of fiducial volume events (light blue). Theνμbackgrounds in the RHC beam sample are much larger than the
analogous ¯νμ backgrounds in the FHC beam sample.
TABLE II. The fractional distributions of true MC interactions for selected events defined at the initial interaction vertex according to the NEUT generator for the FHC beam (left) and RHC beam (right) modes. See text for descriptions of each MC channel.
FHC beam RHC beam
Mode Fraction Mode Fraction
QE 37.83% QE 47.27% 2p2h 3.30% 2p2h 3.19% 1Pi 29.73% 1Pi 24.14% NPi 11.01% NPi 5.05% Meson 1.71% Meson 1.04% DIS 11.27% DIS 2.32% NC 1.50% NC 0.99% ¯νμ 0.33% νμ 11.93% outFV 3.32% outFV 4.05%
tracks are more forward. In Fig. 6 left (right) are the generated MC CCINC events that have a P∅D vertex and a μþ(μ−) track reconstructed in the TPC for the RHC (FHC)
samples. The regions below horizontal lines where θμ< 32° and right of the vertical dash lines where pμ>
500 MeV=c are detector regions that have nonzero accep-tance and reconstructed events for both the FHC and the RHC samples. Hence, we use these two kinematic restric-tions in the cross-section measurements. The resulting reconstructed restricted phase space selection in the νμ mode has 14,398 data events and a corresponding MC sample, scaled to the same data PoT exposure, contains 15,284 events. In the ¯νμ mode, 1,461 data events are selected and a scaled MC sample has 1,634 events. From a study of MC truth selected events, this restricted phase space selection changed the mean value of neutrino
energies below 2 GeV in the FHC sample from 0.83 GeV (unrestricted) to 1.14 GeV (restricted) and in the RHC sample from 0.84 GeV (unrestricted) to 1.08 GeV (restricted). In addition, the νμ and ¯νμ MC samples contained 2.19% and 1.33% events, respectively, whose true kinematic value was outside the restricted phase space region, but its reconstructed value migrated to be inside the restricted phase space region. These events are kin-ematic backgrounds that originated from the same physics process.
V. ANALYSIS METHODS
The number of neutrino interactions in the fiducial volume of the P∅D, Nsignal, can be expressed as the product of the signal cross section per target, σ, the number of
Events 0 50 100 150 200 250 300 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 0 10 20 30 40 50 60 70 80 90 Events 0 200 400 600 800 1000 1200 1400 1600 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 0 10 20 30 40 50 60 70 80 90
FIG. 5. Left (right) two-dimensional plots ofθμversuspμfor RHC (FHC) beam events ofμþðμ−Þ tracks using MC generated CCINC with full acceptance. The vertical and horizontal solid lines correspond toθμ¼ 32° and pμ¼ 500 MeV=c, respectively.
Events 0 20 40 60 80 100 120 140 160 180 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 0 10 20 30 40 50 60 70 80 90 Events 0 50 100 150 200 250 300 350 400 450 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 0 10 20 30 40 50 60 70 80 90
FIG. 6. Left (right) two-dimensional plots ofθμversuspμfor RHC (FHC) beam events ofμþðμ−Þ tracks using MC generated CCINC that have a reconstructed P∅D vertex and TPC muon track. The vertical and horizontal solid lines correspond to θμ¼ 32° and pμ¼ 500 MeV=c, respectively. The restricted phase space cut selection applies to events inside the lower right rectangular region
targets, Ntargets, and the integrated flux, Φ, of incident
neutrinos per unit area, as
Nsignal¼ σNtargetsΦ: ð1Þ
Hence, the cross section becomes σ ¼ Nsignal
ΦNtargets
: ð2Þ
Using our event selection on data, we obtain a candidate signal event sample in our fiducial volume. This process is not 100% efficient and also some nonsignal (background) events are included. To account for this, the MC simulation is used to estimate in our sample the number of background events and the number of signal events. The backgrounds from the FHC (RHC) beam samples include non-CCINC events from the neutrino (antineutrino) beam as well as events created from the antineutrino (neutrino) flux. In addition, the MC simulation generates total number of signal events that were produced. If the rate of restricted phase space selected data events is Ndata
selected and the
predicted number of selected background events is BMC,
the observed number of signal candidates in our fiducial volume is
Nselected signal¼ Ndataselected− BMC; ð3Þ
which include migration events. Next we redefine the selection efficiencyϵ as ϵ ¼ N MC selected signal NMC generated signal : ð4Þ where the NMC
selected signalis the number of signal candidates
whose reconstructed kinematics are in the restricted phase space and NMC
generated signal is the total number of generated
signal events whose true kinematics are in the restricted phase space. We note that NMCselected signal includes a small fraction of migration events as described at the end of
Sec.IV. B. With these definitions, the restricted phase space
signal event rate is Nsignal¼
Ndata
selected− BMC
ϵ : ð5Þ
In Eq.(5), the numerator is the number of signal candidates whose reconstructed kinematics are in the restricted phase space, and this is combined with the denominatorϵ from Eq.(4)to give the proper estimate ofNsignalthat represents the number of signal events whose kinematics are in the true restricted phase space. The neutrino cross section is
σðνμÞ ¼N data
selected− BMC
ϵNtargetsΦ
: ð6Þ
In addition to the cross sections given above, the measured ratio of cross sections Rðν; ¯νÞ and rates rðν; ¯νÞ are defined as Rðν; ¯νÞ ≡σð¯νμÞ σðνμÞ¼ ¯Ndata selected− ¯BMC Ndata selected− BMC ׯϵ ϵ× Φ ¯Φ ð7Þ and rðν; ¯νÞ ≡nð¯νμÞ nðνμÞ¼ ¯Ndata selected− ¯BMC Ndata selected− BMC ׯϵ ϵ: ð8Þ The overlined quantities are obtained from the antineutrino selections as described above and those without overlines represent the neutrino mode selection. Finally, other observables are introduced and defined; the sum Σðν; ¯νÞ, differenceΔðν; ¯νÞ, and asymmetry Aðν; ¯νÞ formed from the νμ and ¯νμ cross sections, as
Σðν; ¯νÞ ≡ σðνμÞ þ σð¯νμÞ; ð9Þ
Δðν; ¯νÞ ≡ σðνμÞ − σð¯νμÞ ð10Þ
and
Aðν; ¯νÞ ≡σðνμÞ − σð¯νμÞ
σðνμÞ þ σð¯νμÞ: ð11Þ
VI. CROSS SECTION AND RATIO SYSTEMATIC ERRORS
The systematic errors on cross sections and ratios of cross sections in this analysis are due to uncertainties on the number of selected background events, the incident neu-trino flux, the number of targets in the detector, and the selection efficiencies. The sources of systematic uncertain-ties can be categorized into three groups: beam flux prediction, neutrino and antineutrino interaction models and detector response. The largest source of uncertainty is due to the beam flux.
A. Beam flux uncertainty
The beam flux uncertainty sources can be separated into two categories: uncertainties of the hadronic interactions, in the graphite target and reinteractions in the horn, and T2K beam line inaccuracies.
The beam flux uncertainty is dominated by the uncer-tainty on the modeling of the hadron interactions, including uncertainties on the total proton-nucleus production cross section, pion and kaon multiplicities, and secondary nucleon production.
The hadronic interactions in the target where the primary proton beam first interacts and produces the majority of the secondary pions is simulated by the FLUKA2011 package which creates MC neutrino and antineutrino flux samples. Uncertainties on the proton beam properties, horn current, hadron production model and alignment are taken into account to produce an energy-dependent systematic uncer-tainty on the neutrino flux. These uncertainties are propa-gated to the T2K neutrino beam flux prediction by reweighting MC flux samples. Systematic uncertainties on the neutrino flux predictions coming from the NA61/ SHINE hadron production measurements are included. Those uncertainties were estimated by varying track selection and identification criteria as well as the param-eters used to calculate needed corrections, to account for example for decays of strange particles like Lambdas, which produce additional pions and protons, that can mimic our signal in the NA61/SHINE detector. Detailed review of the sources of systematics errors of hadron production data of NA61/SHINE results needed for T2K may be found elsewhere [19].
The flux smearing is done using toy MC data sets that are based on the FHC and RHC beam flux uncertainty covari-ance matrices. The resulting1σ change in the cross section is taken as the systematic error associated with the beam flux. These uncertainties on individual cross sections lead to 9% errors whereas the errors on the ratio are 4% due to correlated neutrino and antineutrino flux covariance errors. TableIIIsummarizes the systematic errors due to the beam flux uncertainties on the cross sections and combinations of cross sections. These results have been cross checked with analytic calculations. The fractional errors on ratios have smaller errors due to cancellations of correlated errors between the neutrino and antineutrino modes.
B. Interaction model uncertainty
The interaction model uncertainties were calculated by a data-driven method[26]where the NEUT predictions were compared to external neutrino-nucleus data in the energy region relevant for T2K. Some of the NEUT model parameters are fitted and assigned mean and 1σ error values that allow for differences between NEUT and the external data.
The CCQE model in NEUT is based on the Llewellyn-Smith neutrino-nucleon scattering model[27]with a dipole axial form factor and the BBBA05 vector form factors[28]. The NEUT generator uses the Smith-Moniz RFG model
[29] and includes an implementation of both the random
phase approximation (RPA) correction[30] and the 2p2h Nieves model[30]. The NEUT resonant pion production is based on the Rein-Sehgal model [31] with updated form factors from Ref. [32]. The DIS model used in NEUT includes both the structure function from Ref.[33]and the Bodek-Yang correction [34]. The NEUT MC generator includes various model parameters to describe the different models, uncertainties and approximations. The axial mass MQE
A was set to 1.21 GeV=c2 based on the
Super-Kamiokande atmospheric data and the K2K data. The 1σ error on MQE
A was set to 0.41 GeV=c2. The large
uncertainty on this parameter is due to the disagreements between recent experimental measurements and bubble chamber results[35]. The Fermi gas momentum parameter (pF) values and their errors are set to 223 MeV=c and 225 MeV=c for carbon and oxygen, respectively, with both errors set to12.7 MeV=c. The Fermi gas binding energy (EB) parameter was set to 25 MeV and 27 MeV for carbon
and oxygen, respectively, with both errors set to9 MeV. The Nieves model 2p2h normalization to 1 1 for both carbon and oxygen, the resonant pion production model in NEUT used the Graczyk and Sobczyk form factorsCA5ð0Þ and theI ¼12background scale were set to1.01 0.12 and 1.20 0.20, respectively. The nominal axial mass MRES
A
was set to 0.95 0.15 GeV=c2. Additional uncertainties areνe=νμ cross section factor that was set to1.00 0.02. Both CC and NC coherent uncertainties based on the Rein-Sehgal model were set to1 1 and 1.0 0.3, respectively. Moreover, for CC and NC interactions, additional scale factors were set to0.0 0.4 and 1.0 0.3, respectively. In addition the CC other is an energy dependent factor[20]
and the NC other is a normalization factor. Theπ final state interaction (FSI) uncertainties are tuned to a pion-nucleus scattering data, and other smaller corrections were included[26].
Variation of model parameters within their errors (1σ) was used to estimate their effect on the final observables in order to determine final measurement uncertainties. A summary of the parameters and their effects on the overall normalization are shown in TableIV.
C. Detector response uncertainty
The detector response uncertainty studies used data samples supported with MC samples and measurements of the target weight. The three dominant detector response systematic uncertainties are caused by the fiducial volume boundaries, the sand/rock muon interactions and the mass of the target in the fiducial volume. There were small uncertainties from reconstruction and charge misidentifi-cation from the TPC measurements. All the sources of detector response errors considered in the analysis are given in TableV.
The fiducial volume systematics were estimated by varying its boundaries. The sand/rock muon interactions
TABLE III. Summary table for one standard deviation errors
due to beam flux uncertainties (fractionl errors in %).
σð¯νÞ σðνÞ Rðν; ¯νÞ Aðν; ¯νÞ Σðν; ¯νÞ Δðν; ¯νÞ
occurring upstream and in the surrounding ND280 volume could create tracks passing through the P∅D and TPC detectors, mimicking a CCINC event. Another source of detector systematics was the mass of the target in the fiducial volume. The uncertainty due to the fiducial mass was conservatively estimated to be 0.96% from the mea-sured mass of the detector material during construction and the water mass measured during filling the water bags.
VII. RESULTS A. Cross sections and ratios
The flux averaged cross section and ratio values mea-sured in the FHC and RHC samples are extracted from the
flux, the number of targets, MC efficiencies and MC background estimates. The input parameters are given in TableVI, and the results for the restricted (full) phase space selections are given in Tables VII (VIII). The systematic errors in TableVIIare determined by adding in quadrature the errors in Tables III, IV and V. For example, the fractional R error, taken from the three tables, is 4% and this yields 0.015 for the absolute systematic R error in TableVII.
In Table VI, for the restricted phase space results, the input parameters include the νμð¯νμÞ fluxes normalized to PoT in the FHC(RHC) samples. The number of nucleon targets is given for both the data and MC which slightly differed. The number of reconstructed MC events is given
TABLE IV. Summary table for physics model uncertainties for restricted phase space measurements (fractional errors in %).
Parameter σð¯νÞ σðνÞ Rðν; ¯νÞ Aðν; ¯νÞ Σðν; ¯νÞ Δðν; ¯νÞ MQE A 0.51 0.14 0.37 0.32 0.24 0.08 pFð12CÞ 0.01 0.02 0.01 0.01 0.02 0.02 pFð16OÞ 0 0.01 0 0 0.01 0.01 MEC normð12CÞ 0.30 0.44 0.14 0.12 0.40 0.52 MEC normð16OÞ 0.18 0.24 0.06 0.05 0.22 0.27 EBð12CÞ 0.01 0.01 0.02 0.02 0 0.02 EBð16OÞ 0.01 0.01 0.02 0.02 0 0.02 CA 5ð0Þ 0.70 0.46 0.24 0.21 0.53 0.32 M1π A 0.99 0.28 0.75 0.65 0.44 0.21 I ¼1 2Bkg 0.29 0.21 0.08 0.07 0.23 0.17 νe=νμ 0.02 0 0.01 0.01 0.01 0 CC Other shape 0.65 0.70 0.06 0.79 0.06 0.75 CC Coherent 0.01 0.01 0 0.05 0.69 0.73 NC Coherent 0 0 0 0 0 0 NC Other 1.28 0.39 0.89 0.77 0.63 0.14 π FSI 0.16 0.19 0.11 0.09 0.18 0.23
MEC norm Other 0.08 0.15 0.07 0.20 0.13 0.20
Total 2.13 1.16 1.56 1.36 1.31 1.32
TABLE V. Summary table for detector response uncertainties (fractional errors in %).
Parameter σð¯νÞ σðνÞ Rðν; ¯νÞ Aðν; ¯νÞ Σðν; ¯νÞ Δðν; ¯νÞ
TPC tracking efficiency 0.37 0.32 0.04 0.04 0.34 0.29
Charge misidentification 0.37 0.32 0.04 0.04 0.34 0.29
Sand/Rock muon interference 1.45 2.20 0.74 0.70 1.99 2.70
Fiducial mass 0.96 0.96 0 0 1.36 1.36
Fiducial volume boundaries 0.13 0.97 0.83 1.39 0.77 0.74
Total 1.82 2.63 1.11 1.02 2.58 3.35
TABLE VI. Tabulation of flux, targets, and data/MC events used in the cross section calculations. The data corrected values are background subtracted and divided by the MC efficiency.
Inputs for cross sections Units RHC ¯ν mode FHCν mode
Integrated flux [cm2=1021 PoT] 1.477 × 1013 1.823 × 1013
Number of targets (data) [Nucleons] 3.147 × 1030 3.147 × 1030
Number of targets (MC) [Nucleons] 3.119 × 1030 3.119 × 1030
Number of data/MC events (restricted PS) [Events] 1; 498=1; 634 14; 398=15; 284
Data corrected (restricted PS) [Events=1021 PoT] 41; 821 1; 334 138; 576 1; 249
scaled to the equivalent data PoT. The data/MC generated corrected events are defined as the reconstructed data/MC generated events, minus the MC background and divided by the MC CCINC efficiencies.
In Table VIII, the full phase space results are extrapo-lated by scaling the restricted values in TableVIby the ratio of the total to restricted cross sections as predicted by the NEUT MC generator. The single errors combine the statistical and systematic errors, which included model uncertainties on the assumed values ofMQEA and the 2p2h C12andO16parameters in the scaling factor. The errors on
the νμ and ¯νμ cross sections due to these parameter uncertainties were assumed to be totally uncorrelated leading to a conservative estimate of the systematic errors on the full phase space ratio of cross sections.
The cross section calculations use Eq.(6), and the ratio Rðν; ¯νÞ is obtained from Eq.(7), where we note the number of targets drops out. We find≈10% systematic cross section errors whereas the ratio of cross sectionsRðν; ¯νÞ error has a factor ×2 smaller values of 4.0% errors for the restricted phase space. These systematic errors are mainly due to the flux uncertainties on the flux prediction which have strong correlations between neutrino and antineutrino fluxes which largely cancel in the ratio. The flux predictions for neutrino mode and antineutrino mode are correlated through measurements that are used as inputs to the flux calculation. These measurements include the proton beam current measurement, the measurement of the primary proton interaction rate by NA61/SHINE, and the measure-ment of secondary particle interaction rates by other hadron interaction experiments. The measured ratio of ratesrðν; ¯νÞ given in Eq.(8)represents the ratio ofνμand¯νμevent rates which depends on the integrated FHC and RHC flux and so
its value depends on the particular experiment and data taking periods. The event rate ratio rðν; ¯νÞ fractional systematic uncertainty is the same as cross section ratio Rðν; ¯νÞ, except it does not include the flux errors given in TableIII. The fractional systematic errors are 1.92% for the restricted phase space selections.
B. Discussion of results
In this section, we discuss how our results compare with NEUT predictions, previous measurements, the impact on future CPV measurements and the multinucleon effects that can modify neutrino cross sections.
We observe close agreement between the numbers of data events and the NEUT MC generated events in both the unrestricted and restricted phase space selected events. Using Table VI, the data to MC ratios for the restricted phase space selection for the FHC/RHC modes are 94.2%/91.7%.
We can compare our neutrino result to previous T2K publications that used the FGD subdetector with a scintil-lator target. The previous T2K flux averaged CCINC[6]
was ð6.91 0.13ðstatÞ 0.84ðsystÞÞ × 10−39 cm2 per nucleon and this is within systematic errors to our full phase space measurement in Table VIII. The published T2K CCQE[7]and events of the charged current process that has no pions ðCC0πÞ [36] flux averaged cross sections per nucleon are ð3.83 0.55Þ × 10−39 cm2 and ð4.17 0.05 0.47Þ × 10−39cm2, respectively. In the
context of the NEUT model, the CCINC results presented here are compatible with the CCQE and CC0pi results from these prior publications. These full phase space neutrino results agree with the previous T2K measurements.
The near detector flux averaged uncertainties on the ratio of cross sections and rates are useful to estimate the sensitivity of futureCP conservation tests in long baseline appearance experiments. The restricted phase space frac-tional systematic errors onRðν; ¯νÞ and rðν; ¯νÞ are 4.0% and 1.8%, respectively. These systematic errors on the near detector ratio measurements are now due to many small errors less than 1%, so further substantial improvements will be challenging. Although future measurements of appearance probabilities are likely to be limited by stat-istical uncertainties on far detectorνeand¯νemeasurements, the near detector uncertainties onνμand ¯νμmeasurements may also limit the ultimate precision of future CPV tests. The 2p2h models have been predicted[11]to affect the difference between theνμand¯νμcross sections. The NEUT MC predictions of the νμ and ¯νμ cross sections, their difference and sum, their ratio, and their asymmetry have been calculated in four models: (1) NEUT with a default spectral function[37], (2) RFG model, (3) RFG model with RPA corrections and (4) RFG with RPA corrections and 2p2h interactions. The MC model (4) included 2p2h effects in the NEUT MC generator from the model by Nieves[12], and this model (4) was also used to calculate the TableVI TABLE VII. Restricted phase space cross section and ratio final
results.
Cross sections [×10−39cm2=nucleon]
σð¯νÞ 0.900 0.029 (stat.) 0.088 (syst.) σðνÞ 2.41 0.022 (stat.) 0.231 (syst.) Δðν; ¯νÞ 1.512 0.036 (stat.) 0.152 (syst.) Σðν; ¯νÞ 3.311 0.036 (stat.) 0.318 (syst.) Ratios Rðν; ¯νÞ 0.373 0.012 (stat.) 0.015 (syst.)
Aðν; ¯νÞ 0.457 0.012 (stat.) 0.017 (syst.)
TABLE VIII. Full phase space cross sections and ratio results extrapolated from restricted phase space measurements.
Cross sections [×10−39cm2=nucleon]
σð¯νÞ 1.71 0.29 (stat þ syst)
σðνÞ 7.07 1.20 (stat þ syst)
Ratios
and VII results. The six cross section and ratio measure-ments (solid circles with error bars) are presented in six plots in Figs.7and8. In each plot, the four different model predictions (open squares) are compared for the same measurement. Note each model can have slightly different efficiencies, so the corresponding measurement corrected for efficiency can vary depending upon the particular model. These models include additional nuclear effects such as 2p2h that make different predictions for neutrino and antineutrino enhancements to the cross section. We find different cross section combinations can help differ-entiate the models and here we investigate a limited number of model combinations available in NEUT. The measured cross sections are stable and have negligible changes with
different models. This demonstrates the efficiencies are similar in different models. The observed ¯νμ cross section has slightly better agreement with model 3; however, the other models 1, 2 and 4 predictions are nearly all within 1 standard deviation of the data uncertainties. The numerical values of the model 3 predictions and the data results are given in TableIX. Although the uncertainty on our model combinations is relatively large, it is clear that with higher statistics, such comparisons will be valuable for model separation.
In future T2K measurements, more statistics, especially in the ¯νμ mode, will enable differential water subtracted measurements in bins of muon momentum and angle. After unfolding, the differential measurements of ratios in
TABLE IX. The numerical values of model 3 predictions and the corresponding measurements shown in Figs. 7and8.
Model 3 σð¯νÞ σðνÞ Δðν; ¯νÞ Σðν; ¯νÞ Rðν; ¯νÞ Aðν; ¯νÞ MC predictions 0.908 2.36 1.45 3.26 0.385 0.444 Measurements 0.911 0.094 2.45 0.24 1.55 0.16 3.37 0.33 0.371 0.019 0.459 0.021 MC Model index 1 2 3 4 /nucleon] 2 cm -39 10× ) [ν (σ 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 MC Model index 1 2 3 4 /nucleon] 2 cm -39 10× ) [ν (σ 1.8 2 2.2 2.4 2.6 2.8 3 3.2 MC Model index 1 2 3 4 )ν (σ )/ν (σ 0.32 0.34 0.36 0.38 0.4 0.42 0.44
FIG. 7. Comparison of MC model 1–4 predictions, open squares with no errors bars, to data results, solid circles with error bars, in measurements of cross sectionsσð¯νμÞ [left] and σðνμÞ [middle] and the R ratio σð¯νμÞ=σðνμÞ [right].
MC Model index /nucleon] 2 cm -39 10× ) [ν (σ )+ν (σ 2.6 2.8 3 3.2 3.4 3.6 3.8 4 MC Model index /nucleon] 2 cm -39 10× ) [ν (σ )-ν (σ 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 MC Model index 1 2 3 4 1 2 3 4 1 2 3 4 )ν (σ )+ν (σ )/ν (σ )-ν (σ 0.38 0.4 0.42 0.44 0.46 0.48 0.5 0.52 0.54
FIG. 8. Comparison of MC model 1–4 predictions, open squares with no errors bars, to data results, solid circles with error bars, in measurements of the cross section sum Σ ¼ σðνμÞ þ σð¯νμÞ [left], difference Δ ¼ σðνμÞ − σð¯νμÞ [middle] and asymmetry A ¼ ðσðνμÞ − σð¯νμÞÞ=ðσðνμÞ þ σð¯νμÞÞ [right].
particular, differences and sums are expected to provide improved estimates of systematic uncertainties in future experimental CPV tests and better tests of 2p2h models.
VIII. CONCLUSIONS
In summary, the T2K experiment has measured charged current inclusive events, in a restricted phase space of θμ< 32° and pμ> 500 MeV=c, the flux averaged cross
sections (cm2per nucleon) and ratio of cross sections, as σð¯νÞ ¼ ð0.900 0.029ðstatÞ 0.088ðsystÞÞ × 10−39; ð12Þ σðνÞ ¼ ð2.41 0.021ðstatÞ 0.231ðsystÞÞ × 10−39 ð13Þ and R σð¯νÞ σðνÞ ¼ 0.373 0.012ðstatÞ 0.015ðsystÞ: ð14Þ The¯νμinclusive cross section and the ratioR results are the first published measurements atνμand¯νμflux energies[38]
below 1.5 GeV. Although the current uncertainty on the different model combinations is relatively large, we expect
future higher statistics comparisons will be valuable for model discrimination.
ACKNOWLEDGMENTS
We thank the J-PARC staff for superb accelerator performance. We thank the CERN NA61/SHINE Collaboration for providing valuable particle production data. We acknowledge the support of MEXT, Japan; NSERC (Grant No. SAPPJ-2014-00031), NRC and CFI, Canada; CEA and CNRS/IN2P3, France; DFG, Germany; INFN, Italy; National Science Centre (NCN) and Ministry of Science and Higher Education, Poland; RSF, RFBR, and MES, Russia; MINECO and ERDF funds, Spain; SNSF and SERI, Switzerland; STFC, UK; and DOE, USA. We also thank CERN for the UA1/NOMAD magnet, DESY for the HERA-B magnet mover system, NII for SINET4, the WestGrid and SciNet consortia in Compute Canada, and GridPP in the United Kingdom. In addition, participation of individual researchers and institutions has been further supported by funds from ERC (FP7), H2020 Grant No. RISE-GA644294-JENNIFER, EU; JSPS, Japan; Royal Society, UK; the Alfred P. Sloan Foundation and the DOE Early Career program, USA.
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